cp's OEIS Frontend

A195094 G.f.: Sum_{n>=1} -moebius(2*n)*x^n/(1-x^n)^3.

%I A195094 #10 Mar 30 2012 18:37:28
%S A195094 1,3,5,10,14,18,27,36,39,52,65,68,90,102,100,136,152,150,189,200,198,
%T A195094 250,275,264,310,348,333,396,434,392,495,528,490,592,588,588,702,738,
%U A195094 684,784,860,780,945,980,876,1078,1127,1040,1197,1220,1168,1368,1430,1314,1460,1560,1458,1708
%N A195094 G.f.: Sum_{n>=1} -moebius(2*n)*x^n/(1-x^n)^3.
%C A195094 Compare the g.f. of this sequence to the following identities:
%C A195094 . Sum_{n>=1} -moebius(2*n)*x^n/(1-x^n)^2 = Sum_{n>=1} phi(2*n)*x^n;
%C A195094 . Sum_{n>=1} -moebius(2*n)*x^n/(1-x^n) = Sum_{n>=0} x^(2^n).
%H A195094 Paul D. Hanna, <a href="/A195094/b195094.txt">Table of n, a(n) for n = 1..8200</a>
%F A195094 a(2^n) = 2^(n-1)*(1 + 2^n) for n>=1.
%e A195094 G.f.: A(x) = x + 3*x^2 + 5*x^3 + 10*x^4 + 14*x^5 + 18*x^6 + 27*x^7 +...
%e A195094 where A(x) = x/(1-x^1)^3 + 0*x^2/(1-x^2)^3 - x^3/(1-x^3)^3 + 0*x^4/(1-x^4)^3 - x^5/(1-x^5)^3 + 0*x^6/(1-x^6)^3 - x^7/(1-x^7)^3 + 0*x^8/(1-x^8)^3 + 0*x^9/(1-x^9)^3 + 0*x^10/(1-x^10)^3 - x^11/(1-x^11)^3 +...
%o A195094 (PARI) {a(n)=polcoeff(sum(m=1,n,-moebius(2*m)*x^m/(1-x^m+x*O(x^n))^3),n)}
%K A195094 nonn
%O A195094 1,2
%A A195094 _Paul D. Hanna_, Sep 08 2011